let S be Gene-Set; for p1, p2 being Individual of S holds crossover (p1,p2,0,0,0,0,0) = p2
let p1, p2 be Individual of S; crossover (p1,p2,0,0,0,0,0) = p2
crossover (p1,p2,0,0,0,0,0) = crossover ((crossover (p1,p2,0,0,0,0)),p2,0)
by Th32;
hence
crossover (p1,p2,0,0,0,0,0) = p2
by Th4; verum